Unit 3 check

Unit 3 check: Trigonometric and Polar Functions

10 questions from 5 lessons in Unit 3. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 3.1 · Sort it

No calculator. Each card describes a quantity changing over time. Tap a card, then whether the relationship is periodic.

Periodic

Not periodic

Question 2 · from 3.2 · Match

No calculator. Each angle is in standard position, in radians. Tap an angle, then the angle from 0 up to $2 π$ that shares its terminal ray.

Question 3 · from 3.3 · Calculate

No calculator. A circle of radius 12 is centered at the origin. The terminal ray of an angle of $\frac{2 π}{3}$ radians in standard position meets the circle at $P$ . What is the $x$ -coordinate of $P$ ?

Your answer

Setup for question 4

A point P moves counterclockwise around the unit circle centered at the origin. For an angle $θ$ in standard position, in radians, P is where the terminal ray of $θ$ meets the circle. The table lists P for five angles. Let $V (θ)$ be the vertical displacement of P from the $x$ -axis and $H (θ)$ the horizontal displacement of P from the $y$ -axis. Each is negative when P is below the $x$ -axis or to the left of the $y$ -axis.

The point P for selected angles $θ$
$θ$	P
$- \frac{π}{4}$	$(\frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2})$
$\frac{2 π}{3}$	$(- \frac{1}{2}, \frac{\sqrt{3}}{2})$
$π$	$(- 1, 0)$
$\frac{4 π}{3}$	$(- \frac{1}{2}, - \frac{\sqrt{3}}{2})$
$\frac{11 π}{6}$	$(\frac{\sqrt{3}}{2}, - \frac{1}{2})$

Question 4 · from 3.4 · Calculate

No calculator. What is $V (\frac{4 π}{3})$ ? Give a decimal to three places.

Your answer

Setup for question 5

The function p is sinusoidal. The table gives p at the whole numbers from 0 to 8, and the chart plots more points on its graph. The maximum value of p occurs at $x = 0$ and next at $x = 8$ , and the minimum value between them occurs at $x = 4$ .

Values of the sinusoidal function $p$
$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$p (x)$	$3$	$1 + \sqrt{2}$	$1$	$1 - \sqrt{2}$	$- 1$	$1 - \sqrt{2}$	$1$	$1 + \sqrt{2}$	$3$

Points on the graph of $p$

Each dot is $(x, p (x))$ , at every half unit from 0 to 8, rounded to two decimal places.

Question 5 · from 3.5 · Multiple choice

No calculator. What are the amplitude of p and the midline of the graph of p?

Question 6 · from 3.1 · Multiple choice

No calculator. A periodic function $g$ has the values 2, 5, 3, 5, 2, 5, 3, 5, 2, 5, 3 at $x = 0, 1, 2, \dots, 10$ , in that order. Based on these values, what is the smallest period that fits them?

Question 7 · from 3.2 · Multiple choice

No calculator. The terminal ray of an angle $θ$ in standard position meets the circle of radius 25 centered at the origin at $P = (- 24, 7)$ . Which is true?

Setup for question 8

A Ferris wheel has a radius of 20 meters, and its hub is 22 meters above the ground. Put the origin at the hub, with the positive $x$ -axis pointing horizontally to the right and the positive $y$ -axis pointing straight up, in meters. Each car's position is given by an angle in standard position: the angle, in radians, of the ray from the hub to that car.

Cars on the Ferris wheel
Car	Angle $θ$ (radians)
A	$\frac{π}{3}$
B	$\frac{2 π}{3}$
C	$\frac{7 π}{6}$
D	$\frac{7 π}{4}$

Question 8 · from 3.3 · Match

No calculator. Tap a car on the Ferris wheel of radius 20 meters, then its coordinates relative to the hub, in meters.

Uses the same setup as question 4, above.

Question 9 · from 3.4 · Multiple choice

No calculator. As $θ$ increases from $\frac{2 π}{3}$ to $\frac{4 π}{3}$ , which describes the functions $V$ and $H$ ?

Uses the same setup as question 5, above.

Question 10 · from 3.5 · Calculate

No calculator. What is the frequency of p? Give a decimal.

Your answer

0 of 10 answered.